Home
Class 12
MATHS
The locus of the orthocentre of the tria...

The locus of the orthocentre of the triangle formed by the lines `(1+p) x-py + p(1 + p) = 0, (1 + q)x-qy + q(1 +q) = 0` and y = 0, where `p!=*q`, is (A) a hyperbola (B) a parabola (C) an ellipse (D) a straight line

A

a hyperbola

B

a parabola

C

an ellipse

D

a straight line

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Miscellaneous Exercises

    A DAS GUPTA|Exercise Exercise|77 Videos
  • Pair of Straight Lines and Transformation of Axes

    A DAS GUPTA|Exercise EXERCISE|22 Videos

Similar Questions

Explore conceptually related problems

The locus of the orthocentre of the triangle formed by the lines (1+p)x-py+p(1+p)=0.,(1+q)x-qy+q(1+q)=0 andy =0 wherept (a) a hyperbola (c) an ellipse (b) a parabola (d) a straight line

If a+b+3c=0, c != 0 and p and q be the number of real roots of the equation ax^2 + bx + c = 0 belonging to the set (0, 1) and not belonging to set (0, 1) respectively, then locus of the point of intersection of lines x cos theta + y sin theta = p and x sin theta - y cos theta = q , where theta is a parameter is : (A) a circle of radius sqrt(2) (B) a straight line (C) a parabola (D) a circle of radius 2

Show that the reflection of the line px+qy+r=0 in the line x+y+1 =0 is the line qx+py+(p+q-r)=0, where p!= -q .

The curve represented by the equation sqrt(px)+sqrt(qy)=1 where p,q in R,p,q>0 is a circle (b) a parabola an ellipse (d) a hyperbola

The point of injtersection of the line x/p+y/q=1 and x/q+y/p=1 lies on the line

The equations of the tangents drawn from the origin to the circle x^2 + y^2 - 2px - 2qy + q^2 = 0 are perpendicular if (A) p^2 = q^2 (B) p^2 = q^2 =1 (C) p = q/2 (D) q= p/2

The value of 1.999 ….. In the form of p/q , where p and q are integers and q ne 0 , is

If the lines p_1 x + q_1 y = 1, p_2 x + q_2 y=1 and p_3 x + q_3 y = 1 be concurrent, show that the points (p_1 , q_1), (p_2 , q_2 ) and (p_3 , q_3) are colliner.

If Q(h,k) is the foot of the perpendicular from P(x_(1) ,y_(1)) on the line ax + by+ c=0 then Q(h,k) is

A DAS GUPTA-Objective Tests-Exercise
  1. Let z=x+i y be a complex number where xa n dy are integers. Then, the ...

    Text Solution

    |

  2. Let z=costheta+isintheta. Then the value of sum(m->1-15)Img(z^(2m-1...

    Text Solution

    |

  3. The locus of the orthocentre of the triangle formed by the lines (1+p)...

    Text Solution

    |

  4. Tangents drawn from the point P(1, 8) to the circle x^2+ y^2-6x-4y-11=...

    Text Solution

    |

  5. The normal at a point P on the ellipse x^2+4y^2=16 meets the x-axis at...

    Text Solution

    |

  6. The line passing through the extremity A of the major exis and extremi...

    Text Solution

    |

  7. 36. If vec a, vec b,vec c and vec d are unit vectors such that (vec a ...

    Text Solution

    |

  8. A line with positive direction cosines passes through the point P(2, –...

    Text Solution

    |

  9. If P (3,2,6) is a point in space and Q be a point on the line vecr = (...

    Text Solution

    |

  10. Let f be a non-negative function defined on the interval [0,1]dot If i...

    Text Solution

    |

  11. यदि (sin^(4)x)/2 + (cos^(4)x)/3 = 1/5 ,तब

    Text Solution

    |

  12. for 0ltthetaltpi/2 the solution(s) of sum(m=1)^6c o s e c(theta+((m-...

    Text Solution

    |

  13. In a triangle ABC with fixed base BC, the vertex A moves such that cos...

    Text Solution

    |

  14. The tangent PT and the normal PN to the parabola y^2=4ax at a point P...

    Text Solution

    |

  15. An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The ...

    Text Solution

    |

  16. Let L = lim(x rarr 0) ( a - sqrt( a^2 - x^2) - x^2/4)/x^4, a>0.If L is...

    Text Solution

    |

  17. For the function f(x)=x "cos" 1/x, x ge1

    Text Solution

    |

  18. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  19. The area of the region bounded by the curve y=e^(x) and lines x=0 and ...

    Text Solution

    |

  20. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

    Text Solution

    |